RELATIONS BETWEEN RISK-AVERSE MODELS IN EXTENDED TWO-STAGE STOCHASTIC OPTIMIZATION

We consider an extended two-stage risk-averse stochastic optimization problems in several formulations. Risk-aversion is reflected by risk constraints in form of stochastic-order relations, which are imposed in a time-consistent manner. The problem is analyzed under convexity assumptions. The main goal of this study is to establishing relations between the extended two-stage problem with stochastic-order constraints on the recourse function on the one hand and the two-stage problems with alternative models of risk such as utility functions, distortions, or coherent measures of risk on the other hand.